In a slow cooker, combine the chicken broth with the barley, leek, thyme, 1 1/2 teaspoons of salt and 1/4 teaspoon of pepper. Cook on low until the barley is tender and most of the liquid has been absorbed, about 4 hours. Discard the thyme sprig. Stir in the Parmigiano-Reggiano and butter and season with salt and pepper. Spoon the barley risotto into bowls and serve, passing additional cheese at the table.